Objects in orbit are one example of angular momentum wherein the centrifugal force of the body is balanced with respect to centripetal forces in order to achieve a stable orbit. The angular momentum of a particle is defined as the vector product of the instantaneous values of the position vector and the linear momentum, M=r.times.mv, where M is the Angular momentum of the particle, r is the position vector of the particle, m is the mass of the particle and v is the velocity vector of the particle. For an interacting system of particles, the law of the conservation of angular momentum states that the rate of change of the total angular momentum equals the vector sum of the moments of the external forces applied to the system, d/dt .SIGMA.M.sub.s =.SIGMA.v.sub.s .times.F.sub.s, where the summation is over the particles composing the system. In the absence of external forces, the angular momentum remains constant and no change of configuration can alter the total angular momentum of the system. The principal of conservation applies to angular as well as to linear momentum. Angular momentum being a vector quantity, the principle applies as well to its direction as to its magnitude. The angular momentum of a particle may also be defined as the mass of the particle multiplied by the angular velocity of the particle. While the use of the term "angular velocity" may be extended to any motion of a point with respect to any axis, it is commonly applied to cases of rotation. It is then the vector, whose magnitude is the time rate of change of the angle .theta. which the point is rotated through, i.e., d.theta./dt, and whose direction is arbitrarily defined as that direction of the rotation axis for which the rotation is clockwise. The usual symbol is .omega. or .OMEGA..
The concept of angular velocity is most useful in the case of rigid body motion. If a rigid body rotates about a fixed axis and the position vector of any point P with respect to any point on the axis as origin is r, the velocity v of P relative to this origin is v=.omega..times.r, where .omega. is the instantaneous vector angular velocity.
The average angular velocity may be defined as the ratio of the angular displacement divided by time. Angular acceleration is the time rate of change of the angular velocity, expressed by the vector derivative d.omega./dt. The angular velocity of a body in circular orbit can be altered as a function of changes in the radius r which measures the distance between the center of rotation and the path of the body orbiting about the center. Assume initially that the angular momentum of an object constrained to move in a circular path is constant. As the radius decreases, the tangential velocity vector must increase to conserve angular momentum. Surprisingly, this phenomena has never been applied to hydroelectric power extraction to date.
The following patents reflect the state of the art of which applicant is aware insofar as these patents appear relevant to the instant process. The patents are tendered with the object to discharge applicant's acknowledged duty to disclose relevant prior art. However, it is respectfully stipulated that none of these patents when considered singly or when considered in any conceivable combination teach the nexus of the instant invention especially as set forth hereinbelow and as particularly claimed.
______________________________________ INVENTOR PATENT NO. ISSUE DATE ______________________________________ Lamb, W. 2,546 April 11, 1842 Barnes, W. T. 6,191 March 20, 1849 Winne, C. H. 1,263,983 April 23, 1918 Place, C. I. 2,387,348 October 23, 1945 Hampton, E. N. 2,544,154 March 6, 1951 Weisel, Z. V. 3,071,313 January 1, 1963 Kofink, S. 3,137,477 June 16, 1964 Carson et al. 4,018,543 April 19, 1977 Sanders, Jr. 4,076,448 February 28, 1978 Mysels, K. J. 4,164,382 August 14, 1979 DeMontmorency, D. 4,465,430 August 14, 1984 Komatsu, H. 4,473,931 October 2, 1984 Payne, J. M. 4,508,973 April 2, 1985 Marr et al. 4,512,716 April 23, 1985 ______________________________________
The patent to Hampton is of interest since he teaches the use of a turbine having the greatest coincidental structural similarity with applicant's invention. There shown is a turbine for utilization of expanding compressible fluids (such as steam or gases of combustion) for the rotation of a drive shaft. However, Hampton provides only a compressible fluid which is introduced through an inlet 17 at the narrow end of a plurality of tubular members of helical form. The steam is allowed to expand as it passes from helical cross-sections of smaller diameter to greater diameter. This is the diametrically opposed desiderata of the instant invention. Other structural differences devolve from Hampton's uniting the interior drive shaft of the turbine itself with the helical tubes so that the drive shaft of Hampton is centrally disposed within these tubes and is driven thereby.
The remaining citations show the state of the art further and diverge more starkly from the instant invention.